Mississippi Math C.A.7

MathGrades 9–12Algebra (A) Demonstrate Basic Knowledge of Functions, Including their Behavior and Characteristics

The Standard

Solve mathematical situations and application problems involving or using derivatives, including exponential, logarithmic, and trigonometric functions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Evaluate the Limits and Communicate an Understanding of the Limiting Process

Teacher's field guide

What This Standard Means

What Students Need to Do: Students find derivatives of exponential, logarithmic, and trigonometric functions. They use those derivatives to solve problems about rates of change, turning points, or motion.
What Mastery Looks Like: A student can differentiate e^(2x), ln x, and sin x, using the chain rule when needed. They can explain what a derivative’s sign and units mean in a word problem.
Common Misconceptions: Students may forget the factor of 2 when differentiating e^(2x). Some say the derivative of sin x is -cos x or that ln x stays ln x. Others give a rate without units.
How to Assess It: Exit ticket: A culture has P(t)=100e^(0.2t) bacteria after t hours. Find P'(5) and explain what it means, including units.

Lesson moves

Ways to Teach It

Give pairs a printed graph of y=sin x and rulers to draw tangents at 0 and π/2, then compare slopes with cosine.
Have students compare tangent lines to y=ln x at x=1 and x=4 and explain why the slope shrinks.
Set out cards with e^(2x), ln(3x), and sin(2x) beside derivative cards; pairs match them and explain each chain rule step.
Give students a cooling model, T(t)=20+60e^(-0.3t); they calculate T'(5) and explain what its sign means for temperature.

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